4.23.32 $\sqrt{a^2+b^2{y}^{\prime }(x{)}^2}+x{y}^{\prime }(x)-y(x)=0$

ODE
$$\sqrt{a^2+b^2{y}^{\prime }(x{)}^2}+x{y}^{\prime }(x)-y(x)=0$$ ODE Classification

[[_1st_order, _with_linear_symmetries], _Clairaut]

Book solution method
Clairaut’s equation and related types, main form

Mathematica ✗
cpu = 600.125 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.032 (sec), leaf count = 21

$$\{y\left(x\right)=\sqrt{b^2{\mathit{\_}\mathit{C}\mathit{1}}^2+a^2}+\mathit{\_}\mathit{C}\mathit{1}x\}$$ Mathematica raw input

DSolve[-y[x] + x*y'[x] + Sqrt[a^2 + b^2*y'[x]^2] == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve((a^2+b^2*diff(y(x),x)^2)^(1/2)+x*diff(y(x),x)-y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (_C1^2*b^2+a^2)^(1/2)+_C1*x